Howto use perfect square inside of a imperfect square when finding the square root.?
To use a perfect square inside of an imperfect square when finding the square root, you can follow these steps:
1. Identify the largest perfect square that is smaller than the given imperfect square. For example, if the imperfect square is 18, the largest perfect square smaller than 18 is 16 (4^2).
2. Break down the imperfect square into two parts: the perfect square and the remaining imperfect part. Using our example, 18 = 16 + 2.
3. Express the imperfect square as the sum of the perfect square and the remaining part. In our example, we have 18 = 16 + 2.
4. Take the square root of the perfect square separately. For our example, the square root of 16 is 4.
5. Write down the square root of the perfect square and leave the remaining part under the square root symbol. In our example, it becomes √16 + √2.
6. Simplify if possible. In this case, √16 is already a simplified perfect square root, so we cannot simplify it further.
7. The final answer is √16 + √2.
By using a perfect square inside an imperfect square and splitting it into two parts, you can simplify the square root expression.